The goal of this study is to develop a mathematical model of capillary-tissue oxygen transport more general than the commonly used Krogh cylinder model. The model should allow a description of oxygen transport in a tissue with realistic heterogeneities of blood flow and capillary geometrical parameters. The model will also allow simulation of exchange at the surface of a bounded tissue. Both numerical and analytical methods will be used to simulate three-dimensional oxygen distribution. Results of the theoretical analysis will be compared with the predictions of the Krogh cylinder model and will be tested in specially designed experiments. Experiments will be performed on the isolated cat sartorius muscle and hamster retractor muscle microvascular preparation that assess the contributions of heterogeneities in capillary lengths, intercapillary distances, capillary RBC velocities, and capillary hematocrits on the observed values of tissue PO2 at specific sites in relation to capillary geometry. These experiments should allow for a reasonably clear definition of the magnitude of the oxygen heterogeneities and the mechanisms by which they result. The results from these studies will expand substantially upon previous investigations in which only limited data on oxygen distribution in skeletal muscle have been obtained and no attempts to simulate realistic heterogeneities in the transport parameters have been made. Since previous investigations have shown that O2 transport is linked to skeletal muscle metabolism and blood flow in a regulatory sense, these studies can also serve as a foundation for future work on muscle metabolism and blood flow regulation, thereby allowing a more complete understanding of the factors contributing to peripheral circulatory function and control in normal and pathological states.